1. Field of the Invention
The present invention relates to a method of performing prestack migration of recorded seismic events for imaging a part of an underground zone.
The method according to the invention performs 3D prestack depth migration, for a given velocity model, for imaging the various geologic interfaces or heterogeneities of a part of the substrate.
2. Description of the Prior Art
Prestack migration is a conventional method of processing seismic data. The technique generally consists, knowing the value of a wavefield at known depth, on the surface for example, and a model of the distribution of the wave propagation velocities in the zone, in modelling the propagation of the source field and the retropropagation of the recorded reflection data and in seeking phase coherences between these two modelled fields.
There are three main prestack migation types:
shotpoint migration: the source field is the vibrating state generated by the shotpoint and the reflection data are the response of the subsurface to this source field;
plane wave migration, also called common illumination angle migration: the source field is the plane wave considered and the reflection data are the response of the subsurface to this source field;
offset migation: the source field is the one emitted by a shotpoint and the reflection data are the records obtained by the pickup(s) associated with this shotpoint having the offset considered; in such a migration, migration of the data associated with an offset requires as many wave propagation and retropropagation modellings as there are shotpoints and stacking of the results obtained for each shotpoint.
Examples of implementations of this type of techniques are for example described in:
Claerbout, J. F., 1985; Imaging the Earth""s interior; Blackwell Publications,
Duquet, B., 1996; Amelioration de I""Imagerie Sismique de Structures Gxc3xa9ologiques Complexes; thxc3xa8se, Universitxc3xa9 Paris 13, or
Whitmore, N. D., Felinsky, W. F., Murphy, G. E. and Gray, S. H., 1993; The Application of Common Offset and Common Angle Pre-stack Depth Migration in the North sea, 55th Mtg., EAGE, Expanded abstract.
The main drawback of conventional implementations based on the Kirchhoff equation (or more elaborate versions of this technique, itself based on high-frequency asymptotic techniques) is that they are generally very costly in calculation time because of the volume of the data to be processed and of the results, especially when the velocity field varies laterally (which complicates the arrival time calculations required for implementing this method). For economy reasons, one is often led to limit the volumes of data (by decimation) and/or the amount of results produced (imaged volume of reduced size, rough sampling of the results).
FIG. 6 illustrates an example of a situation which occurs in marine seismic prospection where azimuth moveout correction is necessary. The seismic response of a subterranean formation to seismic waves generated by a seismic source (Si) (an airgun for example) are sensed by receivers (R1 . . . Rji . . . Rn) in a seismic streamer 10 towed by a towing boat 12. Because of a rough sea or currents, the streamer may drift with at least a part of the receivers being out of the route XX following the towing boat 12. As a result of this drift, the azimuth of the directions between the seismic source Si position and at least some of the receivers (Rji) position is not correct. Azimuth moveout correction have also been applied in many other situations in marine seismic prospection when for example several seismic streamers are towed by the towing boat, and also in seismic prospection on land.
In such a typical case, the well-known technique of azimuth moveout correction can be applied for correction of the data obtained from the drifted receivers Rji, which are out of line with the towing boat route XX is used to process the data to convert the data to a form that the data would have been recorded if the receivers were in line with the boat route XX. See xe2x80x9cAzimuth Moveout for 3-D Prestack Imagingxe2x80x9d (pages 1-45) Biondo, Fomel and Chemingui, Jul. 30, 1997 which publication is incorporated herein by reference in its entirety. Azimuth moveout correction has also been applied in many other situations in marine prospection when for example several seismic streamers are towed by the towing boat and also in seismic prospection on land.
The method according to the invention performs migration of seismic data for imaging a part of an underground zone, the seismic data being obtained after a series of Ns seismic reflection cycles comprising each successive emission of elementary wavefields defined each by association of a seismic signal W(t) and of a point of emission in a series of points of emission Si with 1xe2x89xa6ixe2x89xa6Ns, reception, by seismic receivers placed in positions Rji, of the seismic signals reflected by the zone in response to each of these wavefields, and recording of the various signals received by each seismic receiver a time-dependent seismic traces dji(t).
The invention, for a given velocity model, comprises the following steps:
a) applying an azimuth moveout correction to data representing the recorded seismic signal sensed by different seismic receivers located at the points of reception for having all directions between points of emission and points of reception collinear to a common direction.
b) defining a slowness vector p whose two components p1 and p2 can each assume a sequence of previously defined values;
c) defining, for a given slowness vector p and a given point of emission Si, a time lag function t0 (p, i)
d) applying a time lag function t0 (p, i) to each elementary wavefield (associated with point of emission Si) and forming a first surface composite wavefield by spatiotemporal superposition of the various elementary wavefields to which such a time lag is applied;
e) applying a time lag t0 (p, i) to each seismic trace dji(t) marked by the pair (i,j) and forming a surface composite trace field by spatiotemporal superposition of the various seismic traces to which such a time lag is applied;
f) performing migration of the composite trace field using the composite wavefield as the wavefield, by modelling the propagation of the composite wavefield and the retropropagation of the composite trace field and by suitably combining the two composite fields thus modelled at any point of the zone to be imaged;
g) repeating steps c) to e) for all the values assumed by the components p1 and p2 of the vector p; and
h) for any set value of the second component p2 of the vector p, stacking the result of these various combinations so as to obtain a migrated image associated with this set value of p2, thus performing prestack migration.
According to an embodiment, the results obtained can be stacked at g) for all the values assumed by parameter p2, thus performing post-migration stacking.
According to an embodiment, post-migration stacking can be achieved directly without step g).
The method can also comprise updating velocities by analysis of the deformations obtained when the second coordinate p2 of vector p is varied.
According to an embodiment, a migrated image of a part of the zone to be imaged can be formed by using the wave conversion phenomenon, by definition of at least part of the velocity field in P waves and S waves (by applying previously for example preprocessing suited to the data so as to separate the various types of seismic events).
Steps a) to h) can be used for determining the gradient of a cost function involved in an inverse seismic problem.
It is also possible to replace a depth migration by a time migration.
The method of the invention has many advantages:
1) The invention performs migration at an attractive price (calculation cost) because of being independent of the volume of results calculated and of the number of seismic traces recorded, which is unlike conventional Kirchhoff type methods. Only the volume of the zone in which the waves are propagated has an effect on the calculation cost. Volume images are thus obtained by taking account of all the seismic traces at an advantageous cost. This method is considered to decrease by a factor of the order of several tens the calculation time required for 3D prestack migration.
2) The method is applied for velocity models or arbitrary complexity as long as the notion of prestack migration retains its meaning. It is applied without encountering any of the limitations specific to the high-frequency asymptotic techniques (geometric optics) commonly used for 3D prestack migrations.
The method can be implemented by means of conventional wave propagation and retropropagation modelling tools, described for example in the aforementioned book by Duquet B.
Application of the method obtains elementary migrated images associated with a given value of a parameter and the sum of these images (post-migration stack), in the depth domain as well as in the time domain.
In the above method it is assumed that the directions between the emission points Si and the reception points Rji of the receivers are collinear to a common direction. To obtain the initial shot a preprocessing step is applied to the data corresponding to the recorded signals using the well known processing technique of azimuth moveout correction as discussed above. The invention in accordance with the foregoing azimuth moveout correction applies a correction to the data representing the recorded signals having directions between the emission points and the reception points not collinear to a common direction, as described above with reference to the prior art, to compensate for drift of a towed streamer causing the receivers to not be in line with the direction of travel of the towing boat.